Geometric Progression

Write out a series of three or more different whole numbers,
starting from 1, so that the numbers add up to a square.
Thus, 1+2+4+8+16+32=63, but this is just one short of being a
square.

I am only aware of two answers in whole numbers, and these
are easy to discover. I am very interested in any other solutions
that might be found, as well as any algebraic solutions.
Source: Henry Ernest Dudeny, Curious Problems & Puzzles #243